---
title: "mlab-numerics-numeric-ode — Mova code model"
description: "Mova code model of mlab/src/builtins/numeric.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/mlab/src/builtins/numeric.rs.groupant/numeric-ode.groupant/"
---
Elamur: [Mova](https://md.mova.elamur.ai/free/en/) · [Dictionary](https://md.dictionary.elamur.ai/free/en/) · [Research](https://md.research.elamur.ai/free/en/) · **Groupants**

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# mlab-numerics-numeric-ode

The groupant beside mlab/src/builtins/numeric.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.

## Facts

- **kind:** groupant_fragment
- **status:** partial source bound model
- **source:** [`mlab/src/builtins/numeric.rs`](https://github.com/ElamurAI/mova-free/blob/main/mlab/src/builtins/numeric.rs)
- **source SHA-256:** `f6fa5b4a76ef32af…`
- **covers:** ode45 validates output arity/options, gets real tspan/y0 storage, evaluates initial RHS, then adapts Dormand-Prince step using scaled embedded error. Accepted steps append all times when two tspan points, otherwise only requested output targets; RHS must return real vector with neq cells. (bytes 15090–20309)
- **part of:** [mlab-numerics-numeric](https://md.groupants.elamur.ai/free/en/mova/mlab/src/builtins/numeric.rs.groupant/)
- **repository folder:** [`mlab/src/builtins/numeric.rs.groupant/numeric-ode.groupant`](https://github.com/ElamurAI/mova-free/tree/main/mlab/src/builtins/numeric.rs.groupant/numeric-ode.groupant)
- **repository commit:** `855da7bd4a7b`

> **Implementation material.** A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.

## Components

| component | label | where |
|---|---|---|
| **approximant** | partial | [approximant](#approximant) |
| **ast** | partial | `../syntax.json` |
| **cost** | symbolic source derived | [invariant](#invariant) |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [invariant](#invariant) |
| **tests** | executed bounded checks | [tests](#tests) |

## Obernants

The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.

| id | type | label | where |
|---|---|---|---|
| `behavior_complement` | behavior_complement | partial source derived model | [behavior_complement](#behavior-complement) |
| `reverse_reconstruction` | reverse_reconstruction | partial source derived model | [reverse_reconstruction](#reverse-reconstruction) |
| `arity_failure` | arity_failure | partial source derived model | [arity_failure](#arity-failure) |
| `rhs_shape` | rhs_shape | partial source derived model | [rhs_shape](#rhs-shape) |
| `step_acceptance` | step_acceptance | partial source derived model | [step_acceptance](#step-acceptance) |
| `zero_interval` | zero_interval | partial source derived model | [zero_interval](#zero-interval) |

## Model text


### descriptant

#### mlab-numerics-numeric-ode

ode45 validates output arity/options, gets real tspan/y0 storage, evaluates initial RHS, then adapts Dormand-Prince step using scaled embedded error. Accepted steps append all times when two tspan points, otherwise only requested output targets; RHS must return real vector with neq cells.

##### Modeling epoch 2026-10-31

Prospective source reading preceded inline tests. This node records implementation behavior, not a complete MATLAB compatibility contract. Models retain limits discovered in source reading, including real-only projections and warning-only result gates. Synthetic CPU fixtures are independent of frozen suites. No external effects, teacher, corpora or benchmark main are executed.

### approximant

#### Forward relation

ode45 validates output arity/options, gets real tspan/y0 storage, evaluates initial RHS, then adapts Dormand-Prince step using scaled embedded error. Accepted steps append all times when two tspan points, otherwise only requested output targets; RHS must return real vector with neq cells.

Executable Rust surrogate gap: no calibrated replacement is attached. Exact test calls are evidence for the reference, not a fast approximant. Numerical approximants would need a named domain, zero convention and metric at supported caps 1/2/5/10%; categorical errors/effects have no percent surrogate here.

### invariant

#### Invariants and cost

t is directed toward final endpoint on admitted monotone tspan; stored state matrix uses rows=time, columns=equations. No monotonicity validation for arbitrary tspan.

##### Cost

At most1e6 attempted steps; each executes stages plus extra final RHS, O(neq) stage work and O(neq*outputs) storage; callback work external.

Allocation failure, unchecked usize dimension arithmetic and IEEE nonfinite propagation are outside finite fixture guarantees. No measured throughput or global accuracy claim.

### models

## Typed source models: mlab-numerics-numeric-ode

### behavior_complement

nargout1 excludes successful struct output. RHS length mismatch excludes stepping. Rejected steps exclude trajectory append but not callback effects. Nonfinite error or too-small step errors; no dense-output interpolation.

### reverse_reconstruction

A returned table fixes sampled states at times; compatible RHS values must produce accepted stage updates within code's local estimates, but off-stage fields remain unconstrained. Equal-time output can come from any RHS passing initial shape validation.

### arity_failure

Empty args with nargout1 fails struct-output policy before missing-function argument.

### rhs_shape

eval_rhs accepts any real Mat with neq cells, then interprets vector order; complex storage rejects.

### step_acceptance

err<=1 appends accepted y; next factor is5 if zero else clamp(.9*err^-0.2,.2,5).

### zero_interval

Initial RHS still evaluates when tf==t0; while loop skips and returns initial row.


### tests

#### Evidence and limits

Selected wave30_tests exercise this source; fragment-specific limits are stated in its operators.

Native command specifications, numeric exits, profile-paired logs, compiled controls and exact-restoration receipts are retained externally in the wave30 numerics run. Tests exercise actual source, not a copied model. The selected finite fixtures do not prove full convergence, backend accuracy on all matrices, resource exhaustion or side-effectful callback behavior.